An object is thrown upward with some velocity. If the object rises 77.5 m above the point of release, (a) how fast was the object thrown?, (b) How long did it take for the object to reach it's highest point ?

Explanation:

Vertical Launch Upwards

In a vertical launch upwards, an object is launched vertically up from a height H without taking into consideration any kind of friction with the air.

If vo is the initial speed and g is the acceleration of gravity, the maximum height reached by the object is given by:

The object referred to in the question is thrown from a height H=0 and the maximum height is hm=77.5 m.

(a)

To find the initial speed we solve for vo:

(b)

The maximum time or the time taken by the object to reach its highest  point is calculated as follows: